Find the cubes of the first five odd natural numbers and the cube of the first five even natural numbers. What can we say about the parity of the odd cubes and even cubes?

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Solution

Odd cubes
$1^{3} = 1$
$3^{3} = 9$
$5^{3} = 125$
$7^{3} = 343$
$9^{3} = 729$
Even cubes
$2^{3} = 8$
$4^{3} = 64$
$6^{3} = 216$
$8^{3} = 512$
$10^{3} = 1000$
Parity: Cubes of odd numbers is always odd.
Cubes of even numbers is always even.

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Find the cubes of the first five odd natural numbers and the cube of the first five even natural numbers. What can we say about the parity of the odd cubes and even cubes?

Odd cubes 13=1 33=9 53=125 73=343 93=729 Even cubes 23=8 43=64 63=216 83=512 103=1000 Parity: Cubes of odd numbers is always odd. Cubes of even numbers is always even.

Odd cubes
$1^{3} = 1$
$3^{3} = 9$
$5^{3} = 125$
$7^{3} = 343$
$9^{3} = 729$
Even cubes
$2^{3} = 8$
$4^{3} = 64$
$6^{3} = 216$
$8^{3} = 512$
$10^{3} = 1000$
Parity: Cubes of odd numbers is always odd.
Cubes of even numbers is always even.